Atomic Spin Entanglement and Anyonic Statistics in Optical Lattices Zhen-Sheng Yuan （中国科大 苑震生） University of Science and Technology of China USTC KTU, Dec 13, 2018@Kaiserslautern
University of Science and Technology of China (USTC) Frankfurt Beijing USTC, Hefei Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
University of Science and Technology of China (USTC) Peking USTC,Hefei Shanghai Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Shuai Chen Yu-Ao Chen Jian-Wei Pan 潘建伟 包小辉 陈凯 陈帅 陈宇翱 陆朝阳 徐飞虎 Zhen-Sheng Yuan Bo Zhao You-Jin Deng 彭承志 苑震生 赵博 邓友金 张强 张军 刘乃乐 Xing-Can Yao Hanning Dai 朱晓波 霍永恒 姚星灿 汪喜林 郁司夏 戴汉宁 陈腾云 江晓 印娟 任继刚 廖胜凯 李力 Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Introduction to our team Research field: quantum information processing with photons and atoms Quantum communication Free space quantum communication Quantum memory and quantum repeater Metropolitan fiber quantum communication networks Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Introduction to our team Research field: quantum information processing with photons and atoms Quantum computation and simulation with Multi-photon entanglement Superconducting qubit Atom-atom entanglement Ultracold Bose gases (SOC) Ultracold Fermion mixture Ultracold molecule Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Motivation: Quantum Information Processing Resource for QIP, Entangled states Ions: R. Blatt, C. Monroe Photons: Jian-Wei Pan Superconducters: Google, IBM, Intel Ions: Monz et al, PRL 106 , 130506 (2011); N. Friis et al, PRX 8, 021012 (2018); J Zhang et al, Nature 551, 601 (2017) Photons: X-L Wang et al, PRL 117, 210502 (2016); arXiv:1801.04043 Superconducting qubits: P. Roushan et al, Science 358, 1175 (2017) Google; N. Kalb et al, Science 356, 928 (2017), intel Qutech; IBM 49 qubits; Yale; Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Scalability: atoms in optical lattice Optical lattice: an array of in-situ imaging: only one Spin exchange interaction: well coherently controlled atom trapped in a lattice generate spin-spin entanglement cold atoms Multi-atom entanglement! Vaucher et al , NJP (2008) Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Scalability: fault tolerable qubits To overcome qubit errors in quantum computing Error-correcting code • Shor, PRA 52, R2493 (1995) 9qubits • Steane, PRL 77, 793 (1996) 7qubits • Laflamme et al ., PRL 77, 198 (1996) 5qubits Traditional concatenated codes require error rate < 2 10 -5 ! Protect quantum bits/gates at the physical level -- topological quantum computing • Kitaev, Ann. Phys. 303, 2 (2003); Ann. Phys. 321, 2 (2006) • Raussendorf et al ., Ann. Phys. 321, 2242 (2003) • Nayak et al ., RMP 80 (3): 1083 (2008) Relax the error threshold rate from 10 -5 to 10 -2 Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Scalability: fault tolerable qubits Topological Quantum Computation Excited states ∆𝐹 Energy Gap ۧ |𝜔 Ground states Quantum gates--Braiding Anyons Protect qubits with energy gap Anthony James Leggett: … no naturally occurring system is likely to have a Hamiltonian (for topological computing); Purpose- engineered systems of optical lattices or Josephson junction arrays (are promising candidates) Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Kitaev Model: Toric code Protecting qubits with energy gap Hamiltonian: • Four-body interaction • Abelian Anyons: e , m excitaions Kitaev, Annals of Physics 303, 2 (2003) Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Toric code -- Braiding 𝑨 𝜏 𝑘 m e 𝑌 𝜏 𝑘 e m m 𝑌 𝜏 𝑘 m Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Toric code -- Braiding 𝑌 𝜏 4 𝑌 𝜏 3 e |𝜒 = | ۧ ۧ 𝑓, 𝑓, 𝑛, 𝑛 m m 3 4 ห𝜒 ′ = 𝑓 𝑗𝜚 | ۧ ൿ 𝑓, 𝑓, 𝑛, 𝑛 m m m m Topological phase 𝑓 𝑗𝜚 , 𝜚 = 𝜌 e No e -excitation, 𝜚 = 0 𝑌 𝜏 2 2 1 m m m 𝑌 𝜏 1 𝑌 𝜏 𝑘 m Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Spin entanglement and anyonic statistics in OL Our experiment: Manipulating superexchange in optical lattice Creating entangled atom pairs Manipulating four-body interaction, four-atom entanglement Demonstrating anyonic statistics with plaquette units Entangled atom pairs Ring exchange and Toric code Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Atoms in optical lattices Standing wave of light 3D optical lattice Bose-Hubbard model (BHM) J U J : nearest-neighbor tunneling 𝑉 : onsite interactions Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Experimental setup MOT Vacuum chamber BEC Magnetic Transfer BEC Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Prepare a 2D quantum gas with in-situ imaging Lat-Y Pancake-2 11 degree 87 Rb: Load into a pancake trap ۧ |𝐺 = 1, 𝑛 𝐺 = −1 SF to MI transition by BEC 2 × 10 5 atoms 𝑂 2D ~15000, 𝑈 2D =23(3) nK ramping up lattice depth • Objective: NA=0.48, resolution 2 μ m Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Optical super-lattice | ۧ ۧ | ۧ ۧ ↓ = 5𝑇 Τ 1 2 | 𝐺 = 1, 𝑛 𝐺 = −1 ↑ = 5𝑇 Τ 1 2 | 𝐺 = 2, 𝑛 𝐺 = −2 𝑡 cos 2 2𝑙𝑦 + 𝜚 𝑦 + 𝑊 𝑚 cos 2 𝑙𝑦 Isolated double wells: 𝑊 𝑦 = 𝑊 Theory: Duan et al ., PRL 91, 090402 (2003) Experiment: Trotzky et al. , Science 319, 295 (2008) Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Spin super-exchange: generating spin entanglement Interaction dominated 𝑉 ≫ 𝐾 , with pseudo spins: 𝐾 𝑓𝑦 ~ 4𝐾 2 /𝑉 ۧ Initial state: | ↑↓ is degenerate with ۧ | ↓↑ The spins will oscillate between the two configurations with a period of 1/ 𝐾 𝑓𝑦 Stop the oscillation by increasing the barrier to create spin entanglement 1 ۧ ۧ 2 | ↑↓ + | ↓↑ Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Spin-dependent superlattices Normal super-lattice Spin-dependent superlattice angle between two V S polarization planes of + laser S V l | ۧ ۧ Τ | ۧ ۧ Τ ↑ = 5𝑇 Τ 1 2 | 𝐺 = 2, 𝑛 𝐺 = −2 , 𝐺 = 1 2 ↓ = 5𝑇 Τ 1 2 | 𝐺 = 1, 𝑛 𝐺 = −1 , 𝐺 = −1 2 Right Left well is well is higher higher 𝛼𝐶 Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Spin-dependent superlattices Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Spin-dependent superlattices effective magnetic gradient caused by spin-dependent superlattice B 1 B 2 π pulse, ω L B 1 B 2 ω L ω R Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Spin super-exchange: generating spin entanglement 4𝐾 2 𝑊 𝑗 𝑉 • Switch off effective magnetic gradient, | ↑↓ and | ↓↑ degenerate • Decrease 𝑊 𝑗 spin oscillation J/U =0.11, decay 120ms | = V s =16Er s , V l =40Er l • Increase 𝑊 𝑗 Freeze entangled state How to detect entanglement? Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Entanglement detection 1 Entangled state: 𝜔 = 2 ( ↑↓ + ↑↓ ) Spin-dependent collisional loss: identify | ↓↓ from 4 spin basis Imaging spin-up atoms Count N 1 π pulse Merging and killing Count N 2 𝑂 ↓↓ = 𝑂 𝑈𝑝𝑢𝑏𝑚 − 𝑂 1 − 𝑂 2 Identify | ↑↓ , | ↓↑ , | ↑↑ : transfer to | ↓↓ by left/right π pulse Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Detection of entanglement Spin correlation curve Violation of CHSH type Bell’s inequality S = 2.21 ± 0.08 Dai et al., Nature Physics 12, 783 (2016) Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
2D-optical superlattice BHM ： J<<U Super-exchange: Ring-exchange: 𝐈 = 𝑲 𝑻 𝟐 𝑻 𝟑 𝑻 𝟒 𝑻 4 isolated plaquettes B.Paredes & I.Bloch, PRA77,23603 (2008). Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Ring-exchange interaction 𝑦 𝜏 3 𝑦 𝜏 4 𝑦 𝜏 2 𝑦 𝐵 𝑡 = −𝜏 1 4 th order perturbation to the BHM 𝐾 4 𝐼 (4) = 40 ൗ ~Hz 𝑉 3 Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
2D-optical superlattice BHM ： J =200 Hz, U =2 kHz Super-exchange: 𝐾 2 𝑉 = 20 Hz ~ 1 nK 𝐾 𝑓𝑦 ∼ Ring-exchange: 𝐾 4 𝐈 = 𝑲 𝑻 𝟐 𝑻 𝟑 𝑻 𝟒 𝑻 4 𝑉 3 = 0.2 Hz ~ 0.01 nK 𝐾 ∼ Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Minimum toric code Hamiltonian Degenerate ring exchange Toric code model in subspace Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Spectrum of the plaquette model Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Site-resolved addressing: state initialization Effective magnetic gradient created by the spin-dependent superlattices Sawtooth-like, period of OL 𝐶 3 > 𝐶 4 = 𝐶 2 > 𝐶 1 𝐶 4 4 3 3 1 1 2 2 Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Ring Exchange Driven Oscillation Initial state = 1 |𝐵 − + |𝐵 + ۧ ۧ 2 Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Observation of ring exchange driven oscillation Count the populations of different states 𝜌 pulse Imaging, Dark 𝜌 pulse Imaging, Bright Z.-S. Yuan, KTU, DEC.13, 2018@Kaiserslautern
Recommend
More recommend
